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  • Open Access

Efficient learning of lattice gauge theories with fermions

Shreya Shukla*, Yukari Yamauchi†, Andrey Y. Lokhov‡, Scott Lawrence§, and Abhijith Jayakumar∥

  • *Contact author: sshukla@lanl.gov
  • †Contact author: yyamauchi@lanl.gov
  • ‡Contact author: lokhov@lanl.gov
  • §Contact author: srlawrence@lanl.gov
  • ∥Contact author: abhijithj@lanl.gov
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Phys. Rev. D 114, 014514 – Published 28 July, 2026

DOI: https://doi.org/10.1103/xlz6-yzxc

Abstract

We introduce a learning method for recovering action parameters in lattice field theories. Our method is based on the minimization of a convex loss function constructed using the Schwinger-Dyson relations. We show that score matching, a popular learning method, is a special case of our construction of an infinite family of valid loss functions. Importantly, our general Schwinger-Dyson-based construction applies to gauge theories and models with Grassmann-valued fields used to represent dynamical fermions. In particular, we extend our method to realistic lattice field theories including quantum chromodynamics.

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Phys. Rev. D 114, 014514– Published 28 July, 2026
  • Received 6 January 2026
  • Accepted 16 June 2026
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